Look at the flowers on your family heirloom tomato plant. On most heirloom tomatoes the stigmas are closed so the flower can only be pollinated by it self. That's why heirlooms have remained essentially the same for many generations. If the stigma is open then there are bags made to protect the flower you choose and then you use the tomato formed from that flower for your seed source.

Here's a picture to show the stigma difference.

The picture is from Seedsavers Exchange at this link. They'll probably do a better job of explaining.

My family had an heirloom pink tomato which seed was saved from for three generations. That tomato never changed over all that time. Occasionally one sport would be red, but if we saved seed from the red tomato we got pinks from its seed.

It would be much easier to just bag the flowers (bag the entire flower stem) prior to them opening.

Yeah, pick up some organza bags at a craft store (the kind used for bridal party favors and the like) and bag some flower clusters before the flowers open. These bags are cheap, readily available, and work very well.

Note that there are some pollinators that will chew the anther cones and expose the stigmas even in flowers with non-exerted stigmas. There is no such thing as a tomato plant that can never be cross-pollinated in the field. It's not incredibly common, but neither is it really all that rare.

If you want peace of mind, I would bag some blossoms and save seeds only from fruit from the bagged blossoms. It doesn't require much effort at all, and you can be sure the lineage will be preserved.